Let us return to the problem to which our final criticism of existentialist ethics led. Recall that it concerned whether one’s never taking anyone else’s perspective but one’s own when deliberating about what to do is rationally defensible. If Sidgwick had been successful in his attempt to reconcile utilitarianism with egoism, then he would have shown that rationality required following the Principle of Utility. And because following the principle entails taking a general view of one’s circumstances when deliberating about what to do, he would have then shown that always omitting consideration of others’ perspectives when so deliberating would not be rationally defensible. One cannot, after all, follow it without sometimes considering directly how one’s actions will affect others for good or ill. Sidgwick’s failure to reconcile utilitarianism with egoism does not mean, of course, that always omitting consideration of others’ perspectives is rationally defensible, but it does mean that showing it to be rationally indefensible requires an account of deliberation free of the quandary that stymied Sidgwick’s attempt, namely, the dualism of practical reason. The problem, then, is to find an account of deliberation on which practical reason is unified and its exercise yields principles of right action that require one to consider the perspectives of others.

The operation of mapping (naturally occurring) continuous time/analog signals into (electronics-friendly) discrete/digital signals is known as quantization, which is an important subject in signal processing in its own right. In information theory, the study of optimal quantization is called rate-distortion theory, introduced by Shannon in 1959. To start, in Chapter 24 we will take a closer look at quantization, followed by the information-theoretic formulation. A simple (and tight) converse bound is then given, with the matching achievability bound deferred to Chapter 25.

In Chapter 4 we collect some results on variational characterizations of information measures. It is a well-known method in analysis to study a functional by proving variational characterizations representing it as a supremum or infimum of some other, simpler (often linear) functionals. Such representations can be useful for multiple purposes:

• Convexity: the pointwise supremum of convex functions is convex.

• Regularity: the pointwise supremum of lower semicontinuous (lsc) functions is lsc.

• Bounds: the upper and lower bounds on the functional follow by choosing good solutions in the optimization problem.

We summarize the meaning of the Standard Model and present a list of profound open questions within its framework and beyond.

Teleological conceptions of morality originated in ancient Greek philosophy. The major systems of ethics among the ancient Greeks, those of Plato and Aristotle, in particular, were teleological. So too were those of Epicurus and other thinkers who founded important schools of philosophy in the period that came after Plato and Aristotle. Deontological conceptions, by contrast, have a different origin. They derive from an ideal of universal divine law that Christianity drew from the Judaic materials from which it sprang. Christianity, to be sure, drew from the ancient Greeks as well. Its identification of universal divine laws with the laws of nature, for instance, comes from the Stoics, chiefly through Cicero (106–43 BCE). But the ideas in Christianity that yielded deontological conceptions are found in its understanding of divine laws as the laws of a supreme ruler that bind his subjects to obey him in the way that a covenant with him would bind them. These juristic ideas, which originated in Mosaic law, are the original frame for deontological conceptions. The principal text that inspired them is Paul’s statement in Romans: “When Gentiles who have not the law do by nature what the law requires, they are a law to themselves even though they do not have the law. They show that what the law requires is written on their hearts, while their conscience also bears witness and their conflicting thoughts accuse and perhaps excuse them.”

So far we have been focusing on the paradigm for one-way communication: data are mapped to codewords and transmitted, and later decoded based on the received noisy observations. Chapter 23 looks at the more practical setting (except for storage), where the communication frequently goes in both ways so that the receiver can provide certain feedback to the transmitter. As a motivating example, consider the communication channel of the downlink transmission from a satellite to earth. Downlink transmission is very expensive (power constraint at the satellite), but the uplink from earth to the satellite is cheap which makes virtually noiseless feedback readily available at the transmitter (satellite). In general, channel with noiseless feedback is interesting when such asymmetry exists between uplink and downlink. Even in less ideal settings, noisy or partial feedbacks are commonly available that can potentially improve the reliability or complexity of communication. In the first half of our discussion, we shall follow Shannon to show that even with noiseless feedback “nothing” can be gained in the conventional setup. In the process, we will also introduce the concept of Massey’s directed information. In the second half of the Chapter we examine situations where feedback is extremely helpful: low probability of error, variable transmission length and variable transmission power.

Scalar quantum electrodynamics is constructed by promoting a global U(1) symmetry to a local one. We address electrically charged infraparticles, and the corresponding superselection sectors, in infinite volume and in finite volume with two kinds of boundary Conditions.